444 



KRETZ. 



A few words more on this subject may not be amiss. In the 

 first paragraph of this section it is stated that the transformation 

 correction is apphed in order to change a measured distance 

 on the plate into the corresponding actual distance on the sky. 

 That is, however, not all : it does something more than that, when 

 the formulae (12), (17) or ( 1 8), (19) are used. For they presup- 

 pose that all the measured j/'s are multiplied by /, and all the 

 measured a''s by/ sec 0^, where/ is the equatorial scale-value, and 

 f\ is the declination of the center of the plate. But by this pro- 

 cess an error is introduced, as all the distances in right ascen- 

 sion whose declination is greater than 0^ become too small, and 

 I'ice versa. The great advantage in using the formulae men- 

 tioned, is, that they take account of this fact, and permit a con- 

 stant scale-value to be used for all the stars. They include 

 still another correction, namely that due to the curvature of the 

 projections on the plate of the parallels of declination, which 

 are not straight lines, but arcs tangent to the direction of the 

 axis of X, at their intersection with the axis of Y. These con- 

 siderations will explain why the quantities in the table are not 

 symmetrical with respect to the center. 



Table VI. — Transformation Corrections. 



Star. 



, A'a — A' sec ()q 



Af5 — Y 



Star. 



Aa — A'sec 6^ 



_. . 

 A6— V 



I 



II 

 — 10.109 



— ir!'686 



13 



1, 

 +0.688 



—0.233 



2 



— 4-30I 



— 9-603 1 



' 14 



.000 



.000 



3 



+ 20.249 



— 8.028 



15 



—0.003 



.GOO 



4 



— 2.645 



- 3-825 



16 



+0.471 



— 0.176 



5 



—13-245 



— 3-972 , 



17 



—0.059 



— 0.029 



6 



+ I-JI9 



■ — 2.412 : 



18 



+0.026 



—0.321 



7 



— i-ors 



■ — 2.084 



19 



+5644 



-0.938 



S 



+ 1.413 



— 1.599 



20 



+7.140 



—I 323 



9 



+ 9.188 



- 1-366 



21 



+0.046 



1. 916 



10 



! + 7.124 



— 0.655 



22 



+3-567 



— 2.610 



ir 



' - 4585 



— 0.633 



23 



—4-065 



-2.958 



12 



- 3-785 



— 0.503 



24 



-5-781 



—5.046 



Refraction Corrections. — Much has been written on the 

 subject of photographic refraction, and several formulae pub- 

 lished designed to eliminate its effect from the measured rectan- 



(104) 



